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I want to express the following sentence in another way.

The first algorithm was applied to obtain the norm solution by gradually decreasing the value of X.

Can anyone give me some help? Thank you.

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    Your sentence isn't bad. Try rearranging the clauses, see if that helps it flow better. Something like "By gradually decreasing the value of X, the first algorithm was observed to converge on a solution." – John Deters May 21 '15 at 1:34
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The first algorithm was applied over a gradually decreasing value of X to obtain the norm solution

Over is a good word to use when talking about ranges.

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